Sasakian nilmanifolds

Abstract

We prove that a compact nilmanifold admits a Sasakian structure if and only if it is a compact quotient of the generalized Heisenberg group of odd dimension by a co-compact discrete subgroup.

9 pages, to appear in IMRN

References in corpus (3)

• Sasaki-Einstein Manifolds and Volume Minimisation
• Cartan class of Invariant forms on Lie groups
• On the structure of co-Kähler manifolds

Cited by in corpus (7)

• Vaisman nilmanifolds
• A non-Sasakian Lefschetz K-contact manifold of Tievsky type
• The topology of compact Lie group actions through the lens of finite models
• Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds
• Almost formality of quasi-Sasakian and Vaisman manifolds with applications to nilmanifolds
• Hereditary properties of co-Kähler manifolds
• Nilpotent aspherical Sasakian manifolds